CS482/682Artificial Intelligence

Lecture 8:Constraint Satisfaction Problems

and Logic-based Inference

17 September 2009Instructor: Kostas Bekris

Computer Science & Engineering, University of Nevada, Reno

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Search-based Problems

Search ProblemsGiven the state-space, a start state and a successor functionFind a goal state

Local Search Classical Search

• Hill-climbing• Hill-climbing with random restarts• Simulated Annealing• Local Beam Search• Genetic Algorithms

Uninformed• BFS • Uniform-First• DFS• Iterat.-Deep. DFS• Bidirectional

Informed

Best-First Search• Greedy BestFS• A*

Constraint Satisfaction Problems

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Constraint-Satisfaction Problems

Discrete and Finite Domains

•Map-Coloring

•8-queens puzzle

Boolean CSPs

•Satisfiability problems (prototypical NP-Complete problem)

Discrete and Infinite Domains

•Scheduling over the set of integers (e.g., all the days after today)

Continuous Domains

•Scheduling over continuous time

•Linear Programming problems

- Constraints are linear inequalities over the variables

Additional examples:

crossword puzzles, cryptography problems, Sudoku

and many classical NP-Complete problems:

•clique problems, vertex-cover, traveling salesman, subset-sum, hamiltonian-cycle

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Constraint Satisfaction Problem Example

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1. Backtracking Search

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2. Local Search

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1. Backtracking: Forward Checking

WA NT Q NSW V SA T

Initially RGB RGB RGB RGB RGB RGB RGB

After WA=R R G B RGB RGB RGB G B RGB

After Q = G R B G R B RGB B RGB

After V=B R B G R B RGB

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1. Backtracking: Intelligent Backjumping

Assume WA=red and NSW =red, then assign T, NT, Q, SA

SA will cause a conflict, whatever we do...• Where should the algorithm backjump?

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Wumpus World

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Wumpus World

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Wumpus World

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Wumpus World